A spokeswoman for News International declined to comment ahead of a pre-trial hearing which is due to take place on Thursday morning in front of a judge who is set to begin hearing test cases next month.
Many of the settlements are expected to be announced on Thursday, subject to the approval of the judge, Geoffrey Vos.
Gerald Shamash, a lawyer who is representing five high-profile victims including retired soccer star Paul Gascoigne, said all of his claims were being settled, although the deals would probably not be announced as early as Thursday.
"We are in the process of settling them," he told Reuters.
Shamash's other clients with claims against News International are ex-Prime Minister Tony Blair's former spin doctor Alastair Campbell, Phil Hughes, agent to late soccer star George Best, former government minister Elliot Morley and Jimmy Gardner, a friend of Gascoigne's.
News International launched a compensation scheme in November for victims of phone-hacking, promising to pay 10 percent more than the amount considered appropriate by Charles Gray, a former high court judge overseeing the scheme.
It is facing more than 60 claims but the number of possible victims is almost 6,000, according to police.
One lawyer involved said only a handful of low-profile claims were likely to remain after the settlements soon to be announced, meaning public interest in the process would wane.
Much of the sting has been taken out of the civil cases by the judge-led Leveson Inquiry into press ethics and standards, which has already spent months poring over the conduct of all of the British press in detail.
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